<title>Multiclass kernel-based feature extraction</title>

Abstract

Feature Extraction (FE) algorithms have attracted great attention in recent years. In order to improve the performance of FE algorithms, nonlinear kernel transformations (e.g., the kernel trick) and scatter matrix based class separability criteria have been introduced in Kernel-based Feature Extraction (KFE)\cite{}. However, for any L-class problem, at most L-1 nonlinear kernel features can be extracted by KFE, which is not desirable for many applications. To solve this problem, a modified kernel-based feature extraction (MKFE) based on nonparametric scatter matrices was proposed, but with the limitation of only being able to extract multiple features for 2-class problems. In this paper, we present a general MKFE algorithm for multi-class problems. The core of our algorithm is a novel expression of the nonparametric between-class matrix, which is shown to be consistent with the definition of the parametric between-class matrix in the sense of the scatter-matrix-based class separability criteria. Based on this expression of the between-class matrix our algorithm is able to extract multiple kernel features in multi-class problems. To speed up the computation, we also proposed a simplified formula. Experimental results using synthetic data are provided to demonstrate the effectiveness of our proposed algorithm.